A381120 Numbers k such that both A381019(k) and A381019(k+1) are composite.

63, 630, 2423, 5653, 9104, 26308, 36108, 41622, 64526, 85121, 108917, 143913, 148305, 176405, 316974, 399168, 399907, 406487, 536926, 621016, 830793, 937038, 937109, 970243, 1088629, 1480545, 1895503, 3961587, 4651102, 5171081, 5487450, 6219705, 7327856, 8118740

Offset

1,1

Comments

Initially, A381019 consists of runs of primes separated by single composite numbers. These indices k mark the beginning of two or more consecutive composite numbers in A381019.

Links

Table of n, a(n) for n=1..34.

Prog

(PARI) lista(nn) = my(c, f, m=1, q=1, r=0, t, u=List([]), w=vector(nn)); for(n=2, nn, t=0; forprime(p=2, max(m, sqrtint(n)), c=n-1-w[p]; if(c>1&&!w[c], listput(u, c))); listsort(u, 1); for(i=1, #u, c=u[i]; f=factor(c)[, 1]; t=1; for(j=1, #f, if(n-c<=w[f[j]], t=0; break)); if(t, u=u[i+1..#u]; if(r, print1(n-1, ", ")); r=1; w[c]=1; for(j=1, #f, w[f[j]]=n); m=max(m, f[#f]); break)); if(!t, r=0; u=List([]); if(nn>q=nextprime(q+1), w[q]=n))); \\ Jinyuan Wang, Feb 16 2025

Crossrefs

Cf. A381019, A379810 (the values of A381019(k)).

Sequence in context: A390261 A228262 A340902 * A181125 A228221 A022522

Adjacent sequences: A381117 A381118 A381119 * A381121 A381122 A381123

Keyword

nonn

Author

N. J. A. Sloane, Feb 15 2025

Extensions

a(7)-a(8) from Michael De Vlieger, Feb 15 2025

a(9)-a(34) from Jinyuan Wang, Feb 16 2025

Status

approved